I am having a hard time starting on how to calculate this please.
You purchased a $1,000 five percent coupon bond that matures in 10 years.
How much would your bond be worth if interest rates fall to 4% the day after you purchase the bond? What would the bond be worth in one year if interest rates fell to 4% at that point?
To calculate the value of a coupon bond, you will need to use the present value formula, also known as the bond pricing formula. The formula is:
PV = C / (1 + r)^n + M / (1 + r)^n
Where:
PV = Present value (or current worth) of the bond
C = Coupon payment
r = Interest rate
n = Number of periods
M = Maturity value (or face value) of the bond
Let's calculate the present value of the bond if interest rates fall to 4% the day after you purchase the bond.
1. Determine the coupon payment:
The coupon payment is given as five percent of the face value, which in this case is $1,000. Therefore, the coupon payment is $1,000 * 5% = $50.
2. Determine the number of periods:
Since the bond matures in 10 years, the number of periods (n) is 10.
3. Determine the interest rate:
In this case, the interest rate is given as 4%.
4. Determine the present value (PV):
Plug the values into the formula:
PV = $50 / (1 + 4%)^10 + $1,000 / (1 + 4%)^10
Use a calculator or spreadsheet to calculate the present value.
Now let's calculate the value of the bond in one year if interest rates fall to 4% at that point.
1. Determine the coupon payment:
As mentioned earlier, the coupon payment is $50.
2. Determine the number of periods:
Since one year has passed, the number of periods (n) is now 9.
3. Determine the present value (PV):
Use the formula:
PV = $50 / (1 + 4%)^9 + $1,000 / (1 + 4%)^9
Again, use a calculator or spreadsheet to calculate the present value.
By following these steps, you'll be able to calculate the value of the bond at different interest rates and time periods.